Answer :
Using the slope concept, it is found that rhe blade's length is of 90 feet.
What is a slope?
The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, the horizontal change is of 440 feet.
At the highest point, the angle is of 38º, hence:
[tex]\tan{38^\circ} = \frac{h_1}{440}[/tex]
[tex]h_1 = 440\tan{38^\circ}[/tex]
[tex]h_1 = 344[/tex]
At the lowetst point, the angle is of 30, hence:
[tex]\tan{30^\circ} = \frac{h_2}{440}[/tex]
[tex]h_2 = 440\tan{30^\circ}[/tex]
[tex]h_2 = 254[/tex]
Hence, the difference is:
[tex]h_2 - h_1 = 344 - 254 = 90[/tex]
The blade's length is of 90 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
The windmill blade's length, determined using the slope concept, is 90 feet, calculated from measured angles and horizontal distance.
1. Definition of Slope: Slope represents the ratio of vertical change to horizontal change. It's also equivalent to the tangent of the angle of depression.
2. Horizontal Change: Given as 440 feet, the distance from Nick's position to the windmill's base.
3. Calculating Height at the Highest Point:
- The angle at the highest point is 38 degrees.
- Using the tangent function, [tex]\( \tan(38^\circ) \),[/tex] we find the height [tex]\( h_1 \).[/tex]
- The formula is: [tex]\( \tan(38^\circ) = \frac{h_1}{440} \).[/tex]
- Solving for [tex]\( h_1 \), we get \( h_1 = 440 \tan(38^\circ) = 344 \)[/tex] feet.
4. Calculating Height at the Lowest Point:
- The angle at the lowest point is 30 degrees.
- Using the tangent function, [tex]\( \tan(30^\circ) \),[/tex] we find the height [tex]\( h_2 \).[/tex]
- The formula is: [tex]\( \tan(30^\circ) = \frac{h_2}{440} \).[/tex]
- Solving for [tex]\( h_2 \), we get \( h_2 = 440 \tan(30^\circ) = 254 \)[/tex] feet.
5. Difference in Heights:
- We subtract the height at the highest point from the height at the lowest point: [tex]\( h_2 - h_1 = 254 - 344 = 90 \)[/tex] feet.
6. Conclusion:
- According to this method, the windmill blade's length is determined to be 90 feet.
Complete Question:
